Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes

• Main Authors: Colombo, Fabrizio (Author, http://id.loc.gov/vocabulary/relators/aut), Gantner, Jonathan (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2019.
• Edition: 1st ed. 2019.
• Series: Operator Theory: Advances and Applications, 274
• Subjects: Operator theory.; Operator Theory.

This book presents a new theory for evolution operators and a new method for defining fractional powers of vector operators. This new approach allows to define new classes of fractional diffusion and evolution problems. These innovative methods and techniques, based on the concept of S-spectrum, can...

Table of Contents:

• Introduction
• Preliminary results
• The direct approach to the S-functional calculus
• The Quaternionic Evolution Operator
• Perturbations of the generator of a group
• The Phillips-functional calculus
• The H-Infinity -Functional Calculus
• Fractional powers of quaternionic linear operators
• The fractional heat equation using quaternionic techniques.-Applications to fractional diffusion- Historical notes and References
• Appendix: Principles of functional Analysis.